Question: The quadratic $x^2-20x+36$ can be written in the form $(x+b)^2+c$, where $b$ and $c$ are constants. What is $b+c$?
Explanation: We complete the square.

We have $(x-10)^2 = x^2 - 20x + 100$, and so

\begin{align*}
x^2-20x+ 36 &= (x-10)^2 + (36-100) \\
&= (x-10)^2 - 64.
\end{align*}Therefore, $b=-10$ and $c=-64$, which gives us $b+c = \boxed{-74}$.